Caenepeel and Goyvaerts [1]} studied Hom-bialgebras and Hom-Hopf algebras from
a categorical view point, and called them monoidal Hom-bialgebras and monoidal Hom-
Hopf algebras respectively, which are slightly different from the above Hom-bialgebras
and Hom-Hopf algebras.
In [2]}, Makhlouf and Panaite defined Yetter-Drinfeld modules over Hom-bialgebras
and shown that Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation.
Also Liu and Shen [3]} studied Yetter-Drinfeld modules over monoidal Hom-bialgebras and called them Hom-Yetter-Drinfeld modules,
and shown that the category of Hom-Yetter-Drinfeld modules is a braided monoidal categories.
Chen and Zhang [4]} defined the category of Hom-Yetter-Drinfeld modules in a slightly different way to [3]},
and shown that it is a full monoidal subcategory of the left center of left Hom-module category.
